As ultrawide bandwidth (UWB) communication becomes increasingly desirable for wireless devices due to its speed and capacity combined with its resilience to interference within high-frequency bands, it is increasingly necessary to adopt effective error correction and related coding methods for maintaining step with the high accuracy demands associated with UWB communication. It should be noted that a UWB signal may be defined, in accordance with, for example, The Federal Communications Commission “First Report and Order, Revision of Part 15 of the Commission's Rules Regarding Ultra-Wideband Transmission Systems,” ET Docket 98-153, Feb. 14, 2002 as any signal occupying more than 500 MHz in the unlicensed 3.1-10.6 GHz band and meeting a specified energy spectrum or energy spectral density mask. As with many engineering challenges, two predominant constraints guide design activities associated with a UWB system: application speed and power consumption. To address these concerns, various coding schemes can be used to optimize speed and error resiliency while maintaining power consumption at acceptable levels. Thus coding performance and complexity are of great concern in UWB systems.
Convolutional codes are a common choice for coding a continuous sequence of message symbols and provide useful coding performance for UWB systems. For many reasons, convolutional codes can provide power savings due to inherent characteristics of the code and because the error correcting capabilities of the code reduce the requirement for retransmission which can also contribute greatly to saving power on both the transmitter and receiver sides. As will be appreciated by one of ordinary skill, in a convolutional encoder, one message symbol of k bits can be encoded into one code symbol of n code bits, with k and n typically being small integers and with k<n, resulting in a code with a rate of k/n. A typical encoder can be constructed as a shift register plus a series of n connection groups to n summing nodes which produce an n-bit codeword output based on a message symbol input bit and the contents of the shift register. The constraint length K of the encoder is generally taken to be the length of the encoder shift register plus one. Another common parameter used in describing encoders is M which is taken to mean the number of shift register or memory elements. Thus, in the case of a code with a rate of ½, and a constraint length of M=3 (K=4), a typical convolutional encoder for such a code can be described as, for example, a finite state machine (FSM) with 2M, or 8 states.
In a conventional decoder such as a convolutional decoder, maximum likelihood decoder, trellis decoder or the like, used for decoding convolutionally encoded signals, the speed at which at which a codeword can be processed is proportional to the trellis depth, or the number of possible state transitions required to converge on the correct message word. Thus for code symbols received at a code rate rn, a decoding operation must perform fast enough to generate the recovered message symbol at the message symbol rate rk. Since, in a conventional trellis decoder, decisions are made only after the trellis is traversed and the surviving path calculated, the trellis depth can have a large impact on the processing speed required to meet the requirement of generating recovered symbols at the symbol rate. A trellis depths even as short as 2 or 3,double and triple the processing speed required to decode the message symbol at the original message symbol rate leading to unsuitable decoding speeds for high speed transmissions such as transmissions within the UWB symbol rate ranges. Since the trellis depth is a function of the constraint length of the code, and can affect the Forward Error Correction (FEC) capability of the code, along with other desirable features of the code, it would be desirable in the art for a method and apparatus for rapidly decoding a received sequence encoded according to a convolutional code without sacrificing the power savings and other benefits associated with code constraint selection.